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</font><p style="margin: 0in 0in 0pt 0.5in;"><span style='font-family: "Calibri",sans-serif; font-size: 12pt; mso-bidi-font-size: 9.0pt;'><font color="#000000">Important points in
7.5.4:<br style="mso-special-character: line-break;"></font><font color="#000000">
<br style="mso-special-character: line-break;">
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  </font><li style="margin: 0in 0in 0pt; font-style: normal; font-weight: normal; mso-list: l0 level2 lfo1; tab-stops: list 1.0in;"><span style='font-family: "Calibri",sans-serif; font-size: 12pt; mso-bidi-font-size: 9.0pt;'>Understanding
      Discrete vs. Continuous<br style="mso-special-character: line-break;">
      <br style="mso-special-character: line-break;">
      </span></li><font color="#000000" face="Times New Roman" size="3">
  </font><li style="margin: 0in 0in 0pt; font-style: normal; font-weight: normal; mso-list: l0 level2 lfo1; tab-stops: list 1.0in;"><span style='font-family: "Calibri",sans-serif; font-size: 12pt; mso-bidi-font-size: 9.0pt;'>For
      a Continuous Random Variable, probabilities of an interval of values are
      represented by areas (that are sectioned off by vertical slices).<br style="mso-special-character: line-break;">
      <br style="mso-special-character: line-break;">
      </span></li><font color="#000000" face="Times New Roman" size="3">
  </font><li style="margin: 0in 0in 0pt; font-style: normal; font-weight: normal; mso-list: l0 level2 lfo1; tab-stops: list 1.0in;"><span style='font-family: "Calibri",sans-serif; font-size: 12pt; mso-bidi-font-size: 9.0pt;'>For
      a Continuous Random Variable the probability that X=(<i style="mso-bidi-font-style: normal;">any specific value</i>) = 0.<span style="mso-spacerun: yes;">&nbsp;
      </span>For a continuous variable there are an infinite number of possible
      values the variable can have.<span style="mso-spacerun: yes;">&nbsp; </span>Even
      if you think of each one as equally likely (as in a Uniform Distribution),
      the probability of any one particular value is 1/(infinity) which is 0.<br style="mso-special-character: line-break;">
      <br style="mso-special-character: line-break;">
      </span></li><font color="#000000" face="Times New Roman" size="3">
  </font><li style="margin: 0in 0in 0pt; font-style: normal; font-weight: normal; mso-list: l0 level2 lfo1; tab-stops: list 1.0in;"><span style='font-family: "Calibri",sans-serif; font-size: 12pt; mso-bidi-font-size: 9.0pt;'>"<b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;">expected
      value</i></b>" is a term that means the mean (average)<br style="mso-special-character: line-break;">
      <br style="mso-special-character: line-break;">
      </span></li><font color="#000000" face="Times New Roman" size="3">
  </font><li style="margin: 0in 0in 0pt; font-style: normal; font-weight: normal; mso-list: l0 level2 lfo1; tab-stops: list 1.0in;"><span style='font-family: "Calibri",sans-serif; font-size: 12pt; mso-bidi-font-size: 9.0pt;'>the
      mean (“expected value”) is the "balance point" of the area<br style="mso-special-character: line-break;">
      <br style="mso-special-character: line-break;">
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